In case \(W\equiv 1\) , \(\varphi \left( x\right) =x^{p}\) , \(1<p<\infty \) , (REF ) was proved by Marcinkiewicz in Theorem 4.14 of [1]}. For \(W\in A_{p}\) , \(\varphi \left( x\right) =x^{p}\) , \(1<p<\infty \) , (REF ) was
obtained by Kurtz in [2]} and Berkson-Gillespie [3]}.
